I don't think the moral dimension played a part, until Lincoln played it up himself. It was his major message in prosecuting emancipation during the war, and also a plank of his political platform. But I don't think people shared it nearly as strongly.
It took the war, and four years of his use of the bully pulpit in wartime, to drive his message home. I'm sure your Grant quote from April 1861, just as Robert E. Lee was winding up his affairs with the War Department and the U.S. Army, is more typical.
The Virginian antislavery movement withered in the 1820's under the weight of sectional abuse piled atop the calls for abolition from Northern orators. This was a large part of the damage the red-hot Abolitionists did. They made it impossible for Southerners to argue the case themselves, or do anything but close ranks and defend their society.
On that, we agree. Virginia was without doubt the ‘leader’ of the south. In the late 20s and early 30s, there was very strong support for ending slavery in the state --- I seem to recall the legislature being within a handful of votes of actually doing so. But the radical Abolitionists damnations combined with Nat Turner's rebellion, allowed the pro-slavery faction to push the proponents of abolition into a political box from which they could not escape. IMHO, it was one of those tremendous "missed opportunities" of history. If Virginia had ended slavery, even with a gradual phase-out, I think the pressure on the other slave states, especially those of the upper south, to follow Virginia's lead would have been overwhelming.
This brings me back to the abortion debate of today. The antics of outfits like Operation Rescue and the overblown rhetoric of TV preachers like Fallwell push people on the fence over into the other camp. They allow the pro-choice side to paint the vast majority of those opposed to abortion as dangerous radicals. They do far more harm than good. It is for those reasons that I have little regard to Garrison and others who were strident and un-compromising without taking into account the very real political and economic implications of their demands. Lincoln always took a moderate course in regards to slavery until the latter stages of the war. The only area where he was unwilling to compromise was on expansion and on that he had solid constitutional ground.